1 . 
Answer : Option B 
Explanation : 
Nature of roots is determined by discriminant,
D = $b^ 2 – 4ac = (12)^ 2 – 4 x 4 x 9 = 144 – 144 = 0$
$Since D = 0, or b^ 2 = 4ac$
Roots are equal and rational 


2 . 
Answer : Option C 
Explanation : 
log 125 = log $5^ 3$ = 3 log 5 = 3 log $10\over2$ = 3 (log 10 – log 2)
= 3(1 – 0.3010) = 3 (0.6990) = 2.0970. 


3 . 
Answer : Option D 
Explanation : 
$\sqrt{1+sin t\over 1sin t}$ = $\sqrt{{1+sin t\over 1sin t}\times {1+sin t\over 1+sin t} }$ = $\sqrt{(1+sin t2)\over (1+sin 2t)*}$
=$\sqrt {({1+sint\over cos t})}2$ = $1\over cost$ +$ sint \over cost$ = sec t + tan t
Here, *$1 sin^2T = cos^2t$ 


4 . 
Answer : Option A 
Explanation : 
The $1^ {st}$ word will be: EFIW. Keeping position of E fixed, remaining 3 can be arranged in <3 ways = 3 x 2 = 6 ways.
Similarly, we can have another 6 and 6 word with F and I.
Now, $19^ {th}$ word = WEFI, $20^ {th}$ = WEIF, $21^ {st}$ = WFEI,
$22^ {nd}$ = WFIE, $23^ {rd}$ = WIFE and $24^ {th}$ = WIFE. 


5 . 
Answer : Option B 
Explanation : 
Explanation:  log (ab) = log a + log b
Thus, log (1 + 2 + 3) = log 6 and log (1 x 2 x 3) = log 6
But, log (2 + 3 + 4) = log 9 and log (2 x 3 x 4) = log 24 


6 . 
Answer : Option D 
Explanation : 
Required % = $32\over100+32$x 100 = $32\over132$x100 = 24 


7 . 
Answer : Option D 
Explanation : 
160:100 = 8:5
Time taken = 5:8 = 20:32 


8 . 
Answer : Option A 
Explanation : 
There are 2 trains running parallel.
Let relative speed = x m/s
Length of slow train = 30x and of fast = 20x
i.e. Ratio of length = 3:2 = 1:$2\over3$
since slow train in 100m long, fast train = $2\over3$ x 100 = 67m 


9 . 
Answer : Option D 
Explanation : 
Series is: $n^2 + n$ i.e., $1^2+1,2^2+2,3^2+3,etc$
i.e. 2,6,12,20,........
We should have 12 instead of 10. Thus, x = 12
$x^2+$$x\over2$=$12^2$+$12\over2$ = 150 


10 . 
Answer : Option A 
Explanation : 
The series is: 5 + 7 = 12 + 9 = 21, 21 + 11 = 32,
32 + 13 = 45, etc
20 must be replaced by 121
Thus, x = 21
%Gain = $2120\over20$x 100 = 5 



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